The discussion revolves around simplifying a fraction involving variables x, n, and p, where p is defined as the ratio of x to n. Participants are analyzing the expression \(\frac{x}{{p}^{2}}+\frac{n-x}{{(1-p)}^{2}}\) and its transformations.
There is an ongoing examination of the steps taken to simplify the expression, with participants questioning each other's reasoning and the accuracy of the transformations. Some have pointed out potential mistakes in the signs and the interpretation of the original problem statement.
Participants noted a discrepancy regarding the expression involving \(1 - p^2\) versus \( (1 - p)^2\), which has led to confusion in the simplification process. There is also mention of a correction made to the LaTeX formatting of the expression.
HallsofIvy said:No, that is not the right answer. How did you get that?
Why did you combine the fractions and then separate them again? In any case, the problem you posted had [itex]1- p^2[/itex], not [itex](1- p)^2[/itex] which you now have.kulimer said:[itex]=\frac{x{(1-p)}^{2}+{p}^{2}(n-x)}{{p}^{2}{(1-p)}^{2}}[/itex]
[itex]=\frac{x}{{(\frac{x}{n})}^{2}}+\frac{n-x}{{(1-\frac{x}{n})}^{2}}[/itex]
[itex]=x \frac{{n}^{2}}{{x}^{2}}+\frac{n-x}{({\frac{n-x}{n}})^{2}}[/itex]
[itex]=\frac{{n}^{2}}{x}-(n-x)({\frac{n}{n-x}})^{2}[/itex]
[itex]=\frac{{n}^{2}}{x}-\frac{{n}^{2}}{n-x}[/itex]
HallsofIvy said:Why did you combine the fractions and then separate them again? In any case, the problem you posted had [itex]1- p^2[/itex], not [itex](1- p)^2[/itex] which you now have.
You changed a "+" sign above to a "−" sign below.kulimer said:[itex]=\frac{x{(1-p)}^{2}+{p}^{2}(n-x)}{{p}^{2}{(1-p)}^{2}}[/itex]
[itex]=\frac{x}{{(\frac{x}{n})}^{2}}+\frac{n-x}{{(1-\frac{x}{n})}^{2}}[/itex]
[itex]=x \frac{{n}^{2}}{{x}^{2}}+\frac{n-x}{({\frac{n-x}{n}})^{2}}[/itex]
[itex]=\frac{{n}^{2}}{x}-(n-x)({\frac{n}{n-x}})^{2}[/itex]
[itex]=\frac{{n}^{2}}{x}-\frac{{n}^{2}}{n-x}[/itex]
Did I make a mistake somewhere?